DLMF:24.4.E30 (Q7443)

From DRMF
Revision as of 01:28, 2 January 2020 by Admin (talk | contribs) (‎Changed an Item: Add constraint)
Jump to navigation Jump to search
No description defined
Language Label Description Also known as
English
DLMF:24.4.E30
No description defined

    Statements

    Defining formula
    E 2 ⁢ n - 1 ⁡ ( 1 3 ) = - E 2 ⁢ n - 1 ⁡ ( 2 3 ) = - ( 1 - 3 1 - 2 ⁢ n ) ⁢ ( 2 2 ⁢ n - 1 ) 2 ⁢ n ⁢ B 2 ⁢ n , Euler-polynomial-E 2 𝑛 1 1 3 Euler-polynomial-E 2 𝑛 1 2 3 1 superscript 3 1 2 𝑛 superscript 2 2 𝑛 1 2 𝑛 Bernoulli-number-B 2 𝑛 {\displaystyle{\displaystyle E_{2n-1}\left(\tfrac{1}{3}\right)=-E_{2n-1}\left(% \tfrac{2}{3}\right)=-\frac{(1-3^{1-2n})(2^{2n}-1)}{2n}B_{2n},}}
    0 references
    DLMF id
    DLMF:24.4.E30
    0 references
    constraint
    n = 1 , 2 , … 𝑛 1 2 … {\displaystyle{\displaystyle n=1,2,\dots}}
    0 references
    Symbols used
    Q11109
    Defining formula
    B n Bernoulli-number-B 𝑛 {\displaystyle{\displaystyle B_{\NVar{n}}}}
    xml-id
    C24.S2.SS1.m1ajdec
    0 references
     
        Retrieved from "https://drmf-beta.wmflabs.org/index.php?title=Item:Q7443&oldid=31829"